{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# F-theta Scan Lens with Fold Mirror"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "from optiland import optic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "class FTheta(optic.Optic):\n",
    "    \"\"\"F-theta lens\n",
    "\n",
    "    Milton Laikin, Lens Design, 4th ed., CRC Press, 2007, p. 251\n",
    "    \"\"\"\n",
    "\n",
    "    def __init__(self, rotation_angle=0.0):\n",
    "        super().__init__()\n",
    "\n",
    "        angle_rad = np.deg2rad(rotation_angle + 45.0)\n",
    "\n",
    "        # We define the position (x, y, z) instead of only thickness (z)\n",
    "        self.add_surface(index=0, x=0, y=0, z=-np.inf, radius=np.inf)\n",
    "        self.add_surface(index=1, x=0, y=0, z=0.0, radius=np.inf)\n",
    "        self.add_surface(\n",
    "            index=2,\n",
    "            x=0,\n",
    "            y=0,\n",
    "            z=15.0,\n",
    "            rx=-angle_rad,\n",
    "            material=\"mirror\",\n",
    "            is_stop=True,\n",
    "        )\n",
    "        self.add_surface(\n",
    "            index=3,\n",
    "            y=-5.0,\n",
    "            z=15.0,\n",
    "            rx=np.pi / 2,\n",
    "            radius=-2.2136,\n",
    "            material=\"SF57\",\n",
    "        )\n",
    "        self.add_surface(index=4, y=-5.3, z=15.0, rx=np.pi / 2, radius=-2.6575)\n",
    "        self.add_surface(\n",
    "            index=5,\n",
    "            y=-5.32,\n",
    "            z=15.0,\n",
    "            rx=np.pi / 2,\n",
    "            radius=-5.5022,\n",
    "            material=\"SF57\",\n",
    "        )\n",
    "        self.add_surface(index=6, y=-5.8492, z=15.0, rx=np.pi / 2, radius=-3.8129)\n",
    "        self.add_surface(\n",
    "            index=7,\n",
    "            y=-10.1419,\n",
    "            z=15.0,\n",
    "            rx=np.pi / 2,\n",
    "            radius=7.9951,\n",
    "            material=\"SF57\",\n",
    "        )\n",
    "        self.add_surface(index=8, y=-10.7319, z=15.0, rx=np.pi / 2, radius=8.3651)\n",
    "        self.add_surface(index=9, y=-28.7333, z=15.0, rx=np.pi / 2)\n",
    "\n",
    "        # add aperture\n",
    "        self.set_aperture(aperture_type=\"EPD\", value=1.0)\n",
    "\n",
    "        # add field\n",
    "        self.set_field_type(field_type=\"angle\")\n",
    "        self.add_field(y=0)\n",
    "\n",
    "        # add wavelength\n",
    "        self.add_wavelength(value=0.633, is_primary=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We plot the f-theta scan lens for three fold mirror rotation angles:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for angle in [-15 / 2, 0, +15 / 2]:\n",
    "    lens = FTheta(rotation_angle=angle)\n",
    "    lens.draw()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": ".venv",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
